We develop a manifold sampling algorithm for the unconstrained minimization of 4 a nonsmooth composite function f , ψ + h ◦ F when ψ is smooth with known derivatives, h is a 5 nonsmooth, piecewise linear function, and F is smooth but expensive to evaluate. The trust-region 6 algorithm classifies points in the domain of h as belonging to different manifolds and uses this knowl7 edge when computi...

We establish existence, derive necessary conditions, and construct and test an algorithm for the maximization of a column’s Euler buckling load under a variety of boundary conditions over a general class of admissible designs. We prove that symmetric clamped–clamped columns possess a positive first eigenfunction and introduce a symmetric rearrangement that does not decrease the column’s bucklin...

A class of enhancement techniques is proposed for images in arbitrary dimension D. They are free from either space/frequency (scale) or grey references. There are two subclasses. One subclass is the chain: {Negative Laplace operator, Multiplication by Power (γ−1) of modulus-Laplace value, Inverse Negative Laplace operator} together with generalized versions. The generalization of the Negative L...

The idea behind the Clarke Tax Algorithm is that a tax will be assessed to each individual. The amount of this tax depends on how the individual’s utilities affect the rest of the group. Since people do not want to pay taxes, a big assessment will decrease an individual’s overall utility. To get a better understanding of this statement, it is helpful to restrict the problem a bit. Formally, the...

We introduce and study a new class of subdifferentials associated with arbitrary functions. Among the questions considered are: connection with other derivative-like objects (e.g. derivatives, convex subdifferentials, generalized gradients of Clarke and derívate containers of Warga), calculus of approximate subdifferentials and applications to analysis of set-valued maps and to optimization. It...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...